Concept

Auxiliary normed space

Publications associées (26)

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Hypomonotonicity of the Normal Cone and Proximal Smoothness

Grigory Ivanov

We study the properties of the normal cone to a proximally smooth set. We give a complete characterization of a proximally smooth set through the monotonicity properties of its normal cone in an arbitrary uniformly convex and uniformly smooth Banach space. ...

Heldermann Verlag2017

General Proximal Gradient Method: A Case for Non-Euclidean Norms

Volkan Cevher, Ya-Ping Hsieh, Marwa El Halabi, Cong Bang Vu, Van Quang Nguyen

In this paper, we consider composite convex minimization problems. We advocate the merit of considering Generalized Proximal gradient Methods (GPM) where the norm employed is not Euclidean. To that end, we show the tractability of the general proximity ope ...

2017

New Moduli For Banach Spaces

Grigory Ivanov

Modifying the moduli of supporting convexity and supporting smoothness, we introduce new moduli for Banach spaces which occur, for example, as lengths of catheti of right-angled triangles (defined via so-called quasiorthogonality). These triangles have two ...

Tusi Mathematical Research Group2017

Stochastic Spectral Descent for Restricted Boltzmann Machines.

Volkan Cevher

Restricted Boltzmann Machines (RBMs) are widely used as building blocks for deep learning models. Learning typically proceeds by using stochastic gradient descent, and the gradients are estimated with sampling methods. However, the gradient estimation is a ...

2015

The Role of Ocean Space in Contemporary Urbanization

Nancy Raewyn Couling

Although the ocean is investigated by many scientific fields, research about ocean space is scarce. But energy production, extraction of resources, infrastructural and logistical development is increasing incrementally, resulting in a quantum shift in scal ...

EPFL2015

Approximate Matrix Multiplication with Application to Linear Embeddings

Michail Vlachos, Anastasios Kyrillidis

In this paper, we study the problem of approximately computing the product of two real matrices. In particular, we analyze a dimensionality-reduction-based approximation algorithm due to Sarlos [1], introducing the notion of nuclear rank as the ratio of th ...

Ieee2014

A sieve algorithm based on overlattices

Anja Annemone Becker

In this paper, we present a heuristic algorithm for solving exact, as well as approximate, shortest vector and closest vector problems on lattices. The algorithm can be seen as a modified sieving algorithm for which the vectors of the intermediate sets lie ...

Cambridge Univ Press2014

Sparse projections onto the simplex

Volkan Cevher, Christoph Koch, Anastasios Kyrillidis

Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the`1-norm. However, several important learning applications cannot benet from this approach as they feature these convex no ...

JMLR W&CP2013

Time-Optimal Path Following for Robots With Convex-Concave Constraints Using Sequential Convex Programming

Quoc Tran Dinh

Time-optimal path following considers the problem of moving along a predetermined geometric path in minimum time. In the case of a robotic manipulator with simplified constraints, a convex reformulation of this optimal control problem has been derived prev ...

Institute of Electrical and Electronics Engineers2013

-Hyperspectral Image Compressed Sensing Via Low-Rank And Joint-Sparse Matrix Recovery

Pierre Vandergheynst, Mohammad Golbabaee

We propose a novel approach to reconstruct Hyperspectral images from very few number of noisy compressive measurements. Our reconstruction approach is based on a convex minimization which penalizes both the nuclear norm and the l(2,1) mixed-norm of the dat ...

Ieee2012